A new instability of the centrifugal type due to the curvature of external streamlines was theoretically predicted in a recent study on boundary layers along a swept wing. It is, however, not clear how this instability relates to already-known instability phenomena in various three-dimensional flows. So the basic idea developed in the analysis of boundary layers is applied to the simpler problems of the flow on a rotating disk and along the leading edge of a yawed circular cylinder, and the resulting eigenvalue problems are numerically solved to show multiple stability characteristics of the flows. Computational results confirm that the streamline-curvature instability does appear in the rotating-disk flow and that it is in fact identical with the instability called the ‘parallel’ or ‘type 2’ mode in the atmospheric literature. This instability is also found to occur in the steady flow near the attachment line and to give the lowest values of the critical Reynolds number except for a very narrow region close to the attachment line, where the viscous and cross-flow instabilities are dominant. These facts provide evidence to show that the same mode of instability as the classical one observed in rotating flows can appear in general three-dimensional boundary layers without rotation.

Investigated are the fundamental roles of the curvature of external streamlines in the stability of three-dimensional boundary layers, the partial differential equations governing small disturbances superimposed on the basic flows are modeled by a simple system of ordinary differential equations, which include a nondimensional parameter denoting magnitude of the streamline curvature. The eigenvalue problem posed by the model equations is numerically solved to evaluate effects of this parameter on critical Reynolds numbers of the Falkner-Skan-Cooke family of three-dimensional velocity profiles. Computational results predict the possibility of a new instability, essentially due to the streamline curvature, of the centrifugal type similar to the Tayior-Gortler instability caused by a concave curvature of the walL

A theoretical study is presented of the spatial stability of flow in a circular pipe to small but finite axisymmetric disturbances. The disturbance is represented by a Fourier series with respect to time, and the truncated system of equations for the components up to the second-harmonic wave is derived under a rational assumption concerning the magnitudes of the Fourier components. The solution provides a relation between the damping rate and the amplitude of disturbance. Numerical calculations are carried out for Reynolds numbers R between 500 and 4000 and βR [les ] 5000, β being the non-dimensional frequency. The results indicate that the flow is stable to finite disturbances as well as to infinitesimal disturbances for all values of R and βR concerned.

A recent study predicted possibility of existence of a new instability due to the curvature of external streamlines in three-dimensional boundary layers, besides the familiar cross-flow instability, but no reliable evidence of this phenomenon has yet been obtained in experiments. In expectation of dispersive development of the two instabilities, the present study deals with small disturbances induced by continuous forcing from a point source in the boundary layer along a yawed circular cylinder, and attempts to describe their spatial development into wedge-shaped distribution with a linear stability theory, which is applicable to both of the above instabilities. Unlike plane-wave disturbances, the point-source disturbances have an important peculiarity that their propagation is governed by a complex group velocity, and a new method based on the complex property of the group velocity is presented to predict the paths of propagation along which growth rates of disturbances are integrated. Results of this stability calculation clarify important differences in development between the cross-flow disturbances and the streamline-curvature disturbances. These differences will make it possible to observe the new mode of disturbances separately from the other in experiments.

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